String threshold corrections from field theory

A field theory approach to summing threshold effects to the gauge couplings in a two-torus compactification is presented and the link with the (heterotic) string calculation is carefully investigated. We analyse whether the complete UV behaviour of the theory may be described on pure field theory grounds, as due to momentum modes only, and address the role of the winding modes, not included by the field theory approach. "Non-decoupling" effects in the low energy limit, due to a small dimension are discussed. The role of modular invariance in ensuring a finite (heterotic) string result is addressed. (C) 2002 Published by Elsevier Science B.V.